Abstract
In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and uniqueness of the solutions to such RBSDEs in appropriate Banach spaces. The result is established by using some results from optimal stopping theory, some tools from the general theory of processes such as Mertens’ decomposition of optional strong supermartingales, as well as an appropriate generalization of Itô’s formula due to Gal’chouk and Lenglart. In the second part of the paper, we provide some links between the RBSDE studied in the first part and an optimal stopping problem in which the risk of a financial position
Citation
Miryana Grigorova. Peter Imkeller. Elias Offen. Youssef Ouknine. Marie-Claire Quenez. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping." Ann. Appl. Probab. 27 (5) 3153 - 3188, October 2017. https://doi.org/10.1214/17-AAP1278
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